Obama and Romney (heart) women. Who (hearts) them more?

President Obama and GOP rival Mitt Romney had a lot to say about and to women… (Saul Loeb / AFP/Getty Images )

Gentlemen, gentlemen, there’s no reason to fight over us. Really.

Well, in fact, I suppose there is.

It was the undecided voters invited to the town hall at Hofstra University who were the nominal target audience of the presidential debate Tuesday night, but it was women -- the majority of voters and the gender gap that Democrats have relied on, and that Republicans hope to close -- who were being wooed by President Obama and GOP rival Mitt Romney.

So that’s naturally where some of the debate ended up, along with some of the post-game analysis.

Obama’s stances on women’s issues are well known. He favors abortion rights, and the first act he signed into law was the Lilly Ledbetter Fair Pay Act to remedy pay discrimination against women. So when undecided voter Katherine Fenton asked about the wage gender gap, it was a pitch right over the plate for him. It’s clear where he stands, and it’s also clear where he thinks the bulk of female voters stand on these matters.

Romney was the first out of the box to mention women, pointing out that 3.5 million more women now live in poverty under the Obama administration. It’s true. Yet, as Slate magazine says, women in difficult economic times can find themselves harder hit because of wage gaps and the uncertain nature of low-wage and part-time work.

Romney’s other appeals to women were less direct than the president’s, partly because he’s made vulnerable by stances like his plan to cut Headstart programs and to end Obama’s healthcare reform law, which includes no-co-pay contraception coverage.

Romney’s instant inadvertent hit was his reference to "binders full of women." He assigned his gubernatorial staff to go find good female applicants for his Massachusetts Cabinet (and he cited a SUNY Albany study that found he had more women in appointed positions than any other state).

A number of debate watchers seized on Romney’s wonderfully awkward image of binders full of women; by the end of the debate, the phrase had its own Facebook and Tumblr pages. And they seized too on Romney’s conditional "if" in his statement that "I recognized that if you’re going to have women in the workforce, that sometimes you need to be more flexible."

It may have been a poor word choice, but to some viewers, it symbolized a deeper Romney attitude. If? What year is it, again?

Romney’s point about flexibility was a good one, as far as it went, which was not far enough. He boasted that his Massachusetts chief of staff, Beth Myers, who also headed the search committee for Romney’s VP nominee, told Romney that she couldn’t work late because she needed to get home by 5 to make dinner for her children.

That’s fabulous for her -- to have the clout to lay down those rules. But what about most working women -- those who have to work part time and take low-paying jobs and whose only "flexible time" is taking time off without pay to attend to family matters?

And why would Romney stop flexibility at women? Why shouldn’t fathers have flexibility too? This isn’t the "Mad Men" workplace anymore -- or is it in some quarters?

And what about that voter’s question on equal pay? It’s not a question Romney answered, although he spoke a lot about economic opportunities and jobs in general. Equal pay status would give women the leverage to insist on things like the flexible scheduling Romney’s chief of staff enjoyed. And Obamacare would give men and women the chance to get health insurance whether or not they work 40 hours a week, or at a company with its own healthcare coverage. Isn’t that empowering? Doesn’t that boost the workforce?

In the debate, Obama again reached for the economic appeal for women when he declared that equal pay was "not just a women’s issue, this is a family issue, this is a middle-class issue," thereby rounding all the bases on the Democrats’ pitch to female votes.

Romney’s team, Obama said, had punted when asked the candidate’s stance on the Ledbetter act and said it would "get back" to the reporter. Politifact rates this claim as "mostly true." Romney said later that he had "no intention" of changing the law and "certainly support[s] equal pay for women," although by what means, he didn’t say.

It was Obama who also brought up Romney’s pledge to end federal funding for Planned Parenthood -- none of which by law can go to abortion anyway, only to the women’s health services Planned Parenthood provides. And Obama again pitched the larger argument, contending that his healthcare law’s coverage of contraception is not just a health issue, "it’s an economic issue."

To which Romney said something that caught my ear. "Every woman in America should have access to contraceptives." What, exactly, does that mean?